SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
On the Design of a Shape Memory Alloy Spring Actuator
Using Thermal Analysis
SONIA DEGERATU, NICU G. BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA PETRISOR, VASILE DEGERATU
Faculty of Electromechanical Engineering
University of Craiova
Decebal Bd. 107, 200440, Craiova
ROMANIA
[email protected]; [email protected]; [email protected];
[email protected]; [email protected]; [email protected]
Abstract: - Due to their unique properties and behavior, the Shape Memory Alloys (SMAs) play an increasingly
important role in the intelligent systems performance. Recent applications in structural actuation and sensing
demand increased material capabilities.
This paper reviews the main advantages and the properties of SMAs and presents the design strategy for a
typical shape memory actuator configuration of intelligent systems, using as active element Ni-Ti SMA spring
working against a conventional steel spring. It also includes the thermal analysis experiments, in order to
determine the transformation temperatures for the studied SMA spring.
For design optimization a comprehensive graphical interface (based on the thermal analysis results), which runs
under Visual Basic, has been developed for this application. It provides a user friendly environment allowing
intelligent system parameters configuration as well as choosing the most adapted analysis methods and data
displaying.
Key-Words: - SMA, shape memory helical spring, biasing spring, austenite phase, martensite phase,
transformation temperatures
the field of SMAs [3]. Buehler and his co-workers at
the U.S. Naval Ordnance Laboratory discovered the
shape memory effect in an equiatomic alloy of
nickel and titanium, which can be considered a
breakthrough in the field of shape memory materials
(Buehler et al. 1967). This alloy was named Nitinol
(Nickel-Titanium Naval Ordnance Laboratory) [4].
The shape memory effect is often exploited when
SMAs are used as actuators [6] - [15].
In the analyzed system of this paper the shape
memory effect will be exploited to actuate the SMA
spring working against a conventional steel spring
(referred to in this case as the “biasing” spring). The
use of SMA spring as actuator provides the
following advantages: reasonable force/motion
characteristics, a compact size, a high work output,
silent operation, design simplicity, and near step
function operation [4], [5], [13], [14], [16], [17].
Nitinol is the material used for the studied SMA
helical spring, due to its several advantages: very
large recoverable motion, great ductility, excellent
corrosion
resistance,
stable
transformation
temperatures, high biocompatability and the ability
1 Introduction
Shape Memory Alloys (SMAs) are smart materials
that respond with a change in shape, in other words
recovery of strain to changes in external
thermomechanical conditions [1].
Specimens of these materials exhibit two unique
properties [2]:
shape memory effect - the ability of SMAs to be
severely deformed and then returned to their
original shape simply by heating them.
superelasticity or pseudoelasticity - hysteresis
behavior with total strain recovery during a
mechanical loading-unloading cycle.
Both properties are a result of underlying
crystallographic phase transformations [3]. The
aforementioned two main behavioral aspects are
responsible for the exceptional properties that SMAs
possess such as significant internal damping,
extremely high yield stresses and large nonlinear
elastic ranges [4], [5], [6].
Arne Olander first observed the unusual
properties of these alloys, in 1938, but not until the
1960's were any serious research advances made in
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Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
to be electrically heated for shape recovery [4], [5],
[6], [18].
Taking in consideration the advantages and
unique properties of SMAs the authors define the
design strategy for an application using SMA helical
spring as active element, and present the
experimental transformation temperatures obtained
for the Ni-Ti SMA spring by Thermal Analysis
Methods, and a comprehensive graphical interface
running under Visual Basic environment.
Austenite, the stronger phase of shape memory
alloys, occurs at higher temperatures. The shape of
the Austenite structure is ordered, in general cubic,
the structure shown on the left side of Figure 1.
The un-deformed Martensite phase has the same
size and shape as the cubic Austenite phase on a
macroscopic scale, so that no change in size or
shape is visible in shape memory alloys until the
Martensite is deformed.
The thermoelastic martensitic transformation
causes the following properties of SMAs [4].
2 Fundamental characteristics of
SMAs
2.1 One-way shape memory effect
One-way shape memory effect represents the ability
of SMA to automatically recover the high
temperature austenitic shape upon heating, but it is
necessary to apply a force to deform the material in
the low temperature martensitic state.
SMAs are a class of metallic alloys that exhibit a
solid-to-solid phase transition that can be exploited
to achieve a variety of interesting responses [19].
The phase transition (also called martensitic phase
transformation) at the root of SMA behavior occurs
between the high temperature parent phase,
austenite (A), and the low temperature phase,
martensite (M), [3].
When martensite is heated, it begins to change
into austenite and the temperatures at which this
phenomenon starts and finishes are called austenite
start temperature (As) and respectively austenite
finish temperature (Af). When austenite is cooled, it
begins to change onto martensite and the
temperatures at which this phenomenon starts and
finishes are called martensite start temperature (Ms)
and respectively martensite finish temperature (Mf).
Martensite is the relatively soft and easily
deformed phase of shape memory alloys, which
exists at lower temperatures. The molecular
structure in this phase is twinned [4], configuration
shown in the middle of Figure 1. Upon deformation
this phase takes on the second form shown in
Figure 1, on the right.
2.2 Two-way shape memory effect
Two-way shape memory effect or reversible shape
memory effect represents the ability of SMAs to
recover a preset shape upon heating above the
transformation temperatures and to return to a
certain alternate shape upon cooling.
Note that both the one-way and two-way shape
memory effects can generate work only during
heating (i.e. force and motion).
2.3 All-round shape memory effect
All-round shape memory effect is a special case of
the two-way shape memory effect. This effect
differs from the two-way effect in the following
ways [4]:
(I) a greater amount of shape change is possible
with the all-around effect;
(II) the high and low temperature shapes are exact
inverses of each other, that is a complete reversal of
curvature is possible in the case of a piece of shape
memory strip.
2.4 Hysteresis behavior
Due to processes which occur on an atomic scale, a
temperature hysteresis occurs. In other words the
austenite to martensite transformation (the “forward
reaction”) occurs over a lower temperature range
than the martensite to austenite transformation.
Hysteresis is generally defined as the difference
between the temperatures at which the material is
50 % transformed to austenite upon heating and
Fig. 1 Macroscopic and microscopic views of the
two phases of shape memory alloys
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Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
The application presented in this paper uses a
work production operating mode. In this kind of
operating mode a shape memory element, works
against a constant or varying force to perform work.
The element therefore generates force and motion
upon heating. In nearly all practical applications,
force and deflection vary simultaneously as
temperature changes.
In our configuration the SMA helical spring
works against a varying force caused by the steel
spring. With this configuration the SMA spring is
compressed at low temperature by the biasing
spring. At high temperatures the shape memory
spring increases in stiffness, and exerts enough force
to compress the steel spring, giving a net motion or
stroke.
50 % transformed to martensite upon cooling. Most
SMAs have a hysteresis loop width of 10-50oC. It is
important to note that the absolute values of the
transformation temperatures, and the hysteresis
width and shape (“skewness”) all depend to a great
extent on alloy composition and processing.
2.5 Superelasticity
Superelasticity can be defined as the ability of
certain alloys to return to their original shape upon
unloading after a substantial deformation has been
applied. When a shape memory alloy is deformed
above Af and below Md (the temperature above
which stress-induced martensite can no longer be
formed), stress-induced martensite is formed. Then
the material is unloaded, the martensite becomes
unstable and the material returns to austenite and its
original shape.
The loading plateau is the result of the martensite
accommodating the applied stress field. Deformation
along the loading plateau occurs by the growth of
Luder’s bands (highly localized areas of
deformation), which grow in length until they
consume the entire length of the superelastic element.
3.2 Mechanical considerations and design
assumptions
The most successful applications of SMA
components usually have all or most of the
following characteristics [4]:
a mechanically simple design;
the shape memory component "pops" in place
and is held by other parts in the assembly;
the shape memory component is in direct contact
with a heating/cooling medium;
a minimum force and motion requirement for the
shape memory component;
the shape memory component is isolated
("decoupled") from incidental forces with high
variation;
the tolerances of all the components realistically
interface with the shape memory component.
2.6 Vibration damping capacity
Due to the special micro structural behavior, SMAs
exhibit the highest vibration damping property of all
metal materials [15], [19]. The damping is
non-linear and frequency independent, but it’s
sensitive to temperature variations and the
antecedents of thermal cycling.
3 Design Strategy for analyzed system
In the design model the friction effect is
neglected and a linear stress-strain behavior is
assumed.
This article includes the design strategy for the
actuator system comprised of SMA spring and a
conventional steel spring.
The first step an engineer should take when
undertaking a design involving shape memory
material is to clearly define the design requirements.
These usually fall into one of the following
interrelated areas: operating mode, mechanical
considerations, transformation temperatures, force
and/or
motion
requirements,
and
cyclic
requirements [4], [5], [17].
3.3 Experimental transformation
temperatures
The force that a spring of any material produces at a
given deflection depends linearly on the shear
modulus (rigidity) of the material. SMAs exhibit a
large temperature dependence on the material shear
modulus, which increases from low to high
temperature. Therefore, as the temperature is
increased the force exerted by a shape memory
spring increases dramatically [1].
Consequently, it is necessary to find inherent
transformation temperatures, under zero stress
(which depend on the composition, heat treatment
3.1 SMA’s operating modes
The most used operating modes of SMAs are: free
recovery, constrained recovery and work
production [4], [5].
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Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
showing that the sample’s mass does not undergo
any changes at heating and cooling.
Therefore, the TGA curves are ignored in further
measurements.
The heating/cooling sequences to determine
SMA spring material transformation temperatures
are:
heating from 30°C to 100°C at 1°C/min;
holding for 10 min at 100°C;
cooling from 100°C to 15°C at 1 °C/min.
The DTA and DSC curves, for 6.82 mg Ni-Ti
SMA spring material, are presented in Figure 2. By
analyzing this figure we can observe two phase
transitions. The first occurs during the heating,
while the second one appears during the cooling
process. The details of these thermal effects are
presented in Figures 3 and 4 (reported from the DSC
curve).
Figure 3 shows that the determined
transformation temperatures at heating are As=49°C
and Af=56°C. The enthalpy of the endothermal
transition process is ∆Hh=5.7319J/g. The
temperature
corresponding
to
maximum
transformation speed is 51.26°C.
The transformation temperatures at cooling result
from Figure 4: Ms=45°C and Mf=33°C. The
enthalpy of the exothermal transition process is
∆Hc=-4.3810 J/g and the temperature corresponding
to maximum transformation speed is 39.07°C.
and other characteristics of the material), to
establish the real shear modulus values at these
functional temperatures, for a high-quality design.
This section presents the transformation
temperatures obtained for the studied Ni-Ti SMA
helical spring using Thermal Analysis Methods.
Thermal Analysis Methods comprises a group of
techniques in which a physical property of a sample
is measured as a function of temperature, while the
sample is subjected to a controlled temperature
program [20].
Thermogravimetric Analysis (TGA), Differential
Thermal Analysis (DTA) and Differential Scanning
Calorimetry (DSC) methods were used to determine
the required parameters.
TGA is a technique which relies on samples that
decompose at elevated temperatures. The TGA
monitors changes in the mass of sample on heating.
In DTA, the temperature difference that develops
between a sample and an inert reference material is
measured, when both are subjected to identical heattreatments. DTA can be used to study thermal
properties and phase changes.
DSC is the most comprehensive and popular
instrumental
technique
used
in
thermal
characterization of materials [21], [22].
The related technique of DSC relies on
differences in energy required to maintain the
sample and reference at an identical temperature.
The DTA and DSC curves use a system with two
thermocouples. One of them is placed on the sample
and the other on the reference material.
In this paper, both isothermal and non-isothermal
regimes
combined
with
heating-cooling
experiments, were used in order to characterize
SMA test sample.
The measurements were carried out on a Perkin
Elmer Thermo-balance in dynamic air atmosphere,
3.4 Computation algorithm
In the analyzed system the varying force is produced
by a steel spring (Fig. 5). The force which the SMA
spring must now work against varies with
deflection. At low temperature the steel spring is
able to completely deflect the SMA spring to its
compressed length (Fig. 5).
Fig.2 DTA and DSC curves for 6.82 mg Ni-Ti SMA spring material
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Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
Fig. 3 Detail of DSC curve for computation transition at heating of Ni-Ti SMA spring material
Fig. 4 Detail of DSC curve for computation transition at cooling of Ni-Ti SMA spring material
must be as low as possible in order to minimize the
force which the SMA spring must provide to deflect
the biasing spring at high temperature.
When the temperature of the SMA spring is
raised, it expands, compressing the steel spring and
moving, for example, a push-rod.
This method of “biasing” provides a convenient
way of obtaining two-way motion form from a SMA
spring, and is the most common method used in
actuator applications.
Figure 6 shows the parameters involved in the
design of a total system made up of a SMA spring
and a biasing steel spring.
It is assumed that there is no friction present in
the system, in order to simplify the analysis. The
basic problem here is to design a SMA actuator
spring of the smallest force output possible which
will generate the required net output force Fn. This
means that the spring rate of the biasing spring, Kb,
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Fig.5 Two-way motion using a biasing (steel) spring
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Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
∆γ = γ l − γ h = the difference between the low
and high temperature shear strain.
Using the shear moduli at low and high
temperature, Gl and Gh and the maximum shear
stress, Tc, one can compute the shear strains at low
and high temperature and finally the difference ∆γ .
high temperature spring rate [4]
K h = 2588 ⋅ B [N/mm]
where B = d / nc
(3)
3
low temperature spring rate [4]
K l = 345 ⋅ B [N/mm]
Fig.6 SMA spring + biasing spring design diagram
(4)
low temperature length
The minimum spring rate of the biasing spring
will usually be dictated by spatial constraints
(envelope length and diameter), since spring rate is
inversely proportional to the mathematical cube of
the average spring diameter [4], [5].
For this application, the most important relations
of the computation algorithm are presented
hereafter.
L l = d (n + 3) [mm]
(5)
high temperature length
L h = L l + stroke [mm]
(6)
free (manufactured) length
Lf = Lh + P / K h
[mm]
(7)
reset force
r = K l (S + P / K h ) [N]
3.4.1 Shape memory spring
The most important relations involved for the shape
memory spring are:
3.4.2 Biasing spring
The most important relations involved for the
biasing spring are:
wire diameter [5]
d=
8⋅ W ⋅P ⋅c
π ⋅ Tc
[mm]
(1)
bias rate
where:
P = total force required from the SMA spring at
high temperature (P = Fn + Fh);
Fn = required net output force;
Fh = force exerted by the biasing spring;
W = Wahl correction factor;
c = spring index (the average spring diameter, D,
divided by the wire diameter, d). For most shape
memory alloys it is usual to keep the spring index to
a value between six and ten [2], [4];
Tc = maximum shear stress, corrected for coil
curvature
F − Fl
[N/mm]
(9)
Kb = h
stroke
where Fl is the low temperature force which the
biasing spring must exert, equal to the SMA spring
reset force.
bias wire diameter [4]
db = 3
d ⋅S
πD 2 ∆γ
(10)
number of bias active turns [4]
(2)
where:
S = required stroke for the spring;
D = the average spring diameter;
ISSN: 1109-2777
2.55 × Fh × D b
[mm]
T
where:
Db = average bias spring diameter;
T = maximum bias shear stress
Fh = force exerted by the biasing spring
number of active turns [5]
n=
(8)
n=
Gd 4b
8D3b K b
where G is the steel spring shear modulus
1011
(11)
Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
bias spring length at high temperature
38mm and 5.5mm respectively.
Assume that the force exerted by the biasing
spring Fh=2N, the maximum corrected shear stress
Tc=175 MPa, the SMA spring index c=6 and the
low temperature shear strain γl = 0.015 (in order to
ensure a good cyclic life of 50000 cycles).
The transformation temperatures, at heating and
cooling, are those determined at subsection 3.3, that
are Af=56°C and Mf=33°C respectively. For these
temperatures the experimental determined values of
shear modulus are Gh=16890MPa and Gl=3759 MPa
respectively.
Also assume that the two springs are separated
by a plug of thickness 2.5 mm.
Using standard steel spring design procedure,
assume that the maximum shear stress for the wire
is T = 675MPa. The bias spring shear modulus is
G = 79300 MPa.
When the VISUAL BASIC project for SMA
spring with biasing spring design is run, a user
interface is displayed, Figure 7.
First the user has to provide the initial parameters
in the dialogue boxes in the lower part of the
interface. By clicking on the Compute button, the
designed parameters are being displayed for both
SMA spring and biasing spring in the upper part of
L bh = cavity length − plug thickness − L h [mm] (12)
high temperature bias deflection
δ = Fh / K b [mm]
(13)
bias spring free length
L bf = L bh + δ [mm]
(14)
4 Visual Basic application for analyzed
system
A Visual Basic project for the analyzed total
actuator system comprised of SMA spring and
biasing spring was implemented [23]. The list of the
most important relations involved in the background
application computations was already presented at
subsection 3.4.
Below, a numerical example is given illustrating
the abilities of the Visual Basic application.
For the present design example, assume the
following requirements:
a Ni-Ti spring - biasing spring combination is
required providing a net force Fn=3N with an 8mm
stroke;
the maximum cavity length and diameter are
Fig. 7 Dialog interface for SMA spring with biasing spring
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Issue 10, Volume 7, October 2008
SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
Note that the shape memory spring is used to
release the valve mechanism, so it only has to work
against friction.
This type of design allows the shape memory
component to control relatively large forces.
Figure 11 shows how a shape memory spring can
be used to control a bell crank. By changing the
dimensions of the bell crank, to adjust the
mechanical advantage, various combinations of
force and motion can be obtained.
the interface. The total actuator system comprised of
SMA spring and biasing spring is shown in the
middle part of the interface.
When the difference between the cavity length
and the SMA outer diameter becomes smaller than
0.5 mm a warning popup is displayed, Figure 8.
The application also displays a warning popup
when the full compression biasing spring length has
a higher value then the high temperature biasing
spring length, Figure 9.
Fig. 8 Warning popup for SMA outer diameter
Fig. 11 Shape memory Bell Crank Mechanism
Figure 12 shows a typical valve application in
which the fluid flow is perpendicular to the action of
the shape memory spring.
Figure 13 shows a valve application in which the
fluid flow is parallel to the action of the shape
memory spring.
Fig. 9 Warning popup for high temperature
biasing spring length
5 Applications of SMA spring with
biasing spring configuration
The analyzed configuration is frequently used for
SMA Latching Mechanisms, for SMA Bell Crank
Mechanisms [4], [5], and for SMA Controlled
Valves developed in our laboratory and used in the
robotic field [4], [24], [25], [26].
Figure 10 illustrates the operation of a latching
valve, which could be used as a safety mechanism to
cut off gas flow in the event of a fire or an extreme
temperature increase.
Fig. 12 Shape memory controlled valve, perpendicular
action mode
Fig. 13 Shape memory controlled valve, parallel
action mode
Fig. 10 Shape memory Latching Mechanism
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BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
Applications. Universitaria Press, 2003,
Craiova, Romania.
[6] M. Dolce, D. Cardone, Mechanical Behavior
of Shape Memory Alloys for Seismic
Applications 2: Austenitic NiTi Wires
Subjected to Tension. Int. Met. Schi, 43, 2001.
[7] L. J. Garner, L. N. Wilson, D. C. Lagoudas,
Development of a shape memory alloy actuated
biomimetic vehicle. Smart Structures and
Materials, 9(5): 673–683, October 2000.
[8] J. K. Strelec, et al, Design and Implementation
of a Shape Memory Alloy Actuated
Reconfigurable Airfoil, Journal of Intelligent
Material Systems and Structures, Vol. 14,
No. 4-5, 2003.
[9] N. G., Bizdoaca, S. Degeratu, C. Pana, C.
Vasile,
Fuzzy
Logic
Controller
for
Hyperredundant Shape Memory Alloy Tendons
Actuated Robot. Proceedings of 7th
International Carpathian Control Conference.
Ostrava Beskydy, Czech Republic, 29-31 May,
2006, ISBN 80-248-1066-2, pp-53-56.
[10] N. G. Bizdoaca, S. Degeratu, M. Niculescu, D.
Pana, Shape Memory Alloy Based Robotic
Ankle. Proceedings of 4th International
Carpathian Control Conference, 2004, vol. I,
May 25-28, Zakapone, Poland, ISBN 8389772-00-0,
pp. 715-720.
[11] N. Vincenzo, R. Cesare, S. Savino, Perspective
Transform in Robotic Applications. WSEAS
Transactions on Systems, Issue 4, Volume 5,
April 2006, ISSN 1109-2777, pp. 678-685.
[12] R. Jong-Seok Rho, J. Hyun-Kyo, The
Characteristic Analysis of a Nano Positioning
Actuator. WSEAS Transactions on Systems,
Issue 4, Volume 6, April 2007, ISSN 11092777, pp. 669-668.
[13] N. G. Bizdoaca, S. Degeratu, et al., Robotic
Finger Actuated with Shape Memory Alloy
Tendon. WSEAS Proceedings of Soft
Computing, Optimization, Simulation &
Manufacturing Systems, 2003, Malta, ISSN
1107–2653, pp. 897-906.
[14] N. G. Bizdoaca, S. Degeratu, et al, Shape
Memory Alloy Tendons Actuated Tentacle
Robotic Structure - Models and Control, ISI 5th
International Conference on Informatics in
Control, Automation and Robotics, ICINCO
2008, Volume 2, May, Madeira, Portugalia
ISBN 978-989-8111-31-9, pp. 77-80.
[15] G. Kulvietis, I. Tumasoniene, D. Mazeika, The
Design of the Multicomponent Ultrasonic
Actuators on the Basis of Mode - Frequency
Analysis. WSEAS Transactions on Systems,
6 Conclusions
The paper presents the design strategy of a shape
memory actuator configuration (SMA spring with
biasing spring), for which the authors defined: the
operating mode, the mechanical considerations, the
design assumptions and the computation algorithm.
Using Thermal Analysis Methods the authors
determined the experimental transformation
temperatures for the Ni-Ti SMA spring material.
These temperatures were necessary to precisely
establish the shear modulus values for a high-quality
design.
In addition, for this design strategy, a Visual
Basic application was developed, providing:
adequate dialogue boxes for fast and easy initial
parameters configuration;
fast computation and display of all required
information for a complete SMA element design;
warning popup when the maximum imposed
value of a parameter is exceeded;
remarkable facilities to analyze results and
choose an optimal solution.
This Visual Basic application is already used by
the Institute of Research ICMET Craiova for
engineering purposes and by the Faculty of
Electromechanical Engineering of Craiova for
didactical ones.
Acknowledgment
This work was supported by the National University
Research Council (CNCSIS) of the Romanian
Minister of National Education. It is part of a project
covering theoretical and applicative researches on
SMA actuators used in the robotic field.
References:
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[3] K. Otsuka, C. M. Wayman, Shape Memory
Materials. Cambridge University Press, 1999,
chapter 2.
[4] T. C. Waram, Actuator Design Using Shape
Memory Alloys. Ontario Press, 1993, Canada.
[5] S. Degeratu, N. G. Bizdoaca, Shape Memory
Alloys. Fundamental Notions, Design and
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SONIA DEGERATU, NICU G.
BIZDOACA, GHEORGHE MANOLEA,
ILIE DIACONU, ANCA P., VASILE DEGERATU
WSEAS TRANSACTIONS on SYSTEMS
[22] J. Cao and I. Sbarski, Determination of the
enthalpy of solid phase transition for isotactic
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